What is the reason why we do not count integers for sig figs?
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What is the reason why we do not count integers for sig figs?
I learned that for integers/exact numbers such as 70 or 80, you do not count the number of sig figs because it is an exact number. Can someone explain this rule to me and the reason why we do not count those sig figs? Does that rule also apply to integers such as 65 and 53 (since these have two sigs figs?)

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Re: What is the reason why we do not count integers for sig figs?
You do count integers for sig figs. Any nonzero integer is a significant figure so both 70 and 80 would have 1 significant figure each while 65 would have 2 because there are 2 nonzero digits. All nonzero digits are significant. Zeroes are only significant if they follow a decimal point or are in between two nonzero digits. So a number like 303 would have 3 sig figs since the zero is in between two nonzero digits.

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Re: What is the reason why we do not count integers for sig figs?
Chesca Legaspi 2F wrote:You do count integers for sig figs. Any nonzero integer is a significant figure so both 70 and 80 would have 1 significant figure each while 65 would have 2 because there are 2 nonzero digits. All nonzero digits are significant. Zeroes are only significant if they follow a decimal point or are in between two nonzero digits. So a number like 303 would have 3 sig figs since the zero is in between two nonzero digits.
I thought we do count integers as well, but today a UA specifically said that if there are whole numbers/integers in a problem without a decimal, you do not count it for sig figs since integers are ambiguous. I was a bit confused about that idea though, so I was hoping for an explanation. For example, if a problem had the number 70, it would make the final answer less accurate because we would only be counting one sig fig. That's what I initially thought was the reason why we don't count integers.

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Re: What is the reason why we do not count integers for sig figs?
I think integer as a result of measurements are counted for sig figs, and the rules have been answered by previous students. Exact numbers derived from counting or integers that are defined numbers, however, aren't counted for sig fig because they do not affect the accuracy of calculation nor precision of expression. Say you counted 10 people in a room, you can express that with 10.0000 or 10.0000000000. Therefore technically there are an infinite number of sig figs in exact numbers so we just omit them entirely. However, if you measured the mass of an element to be 10 grams, you can't express that as 10.0 because the machine used is not calibrated to express the tenth; it would be inaccurate to assume that the digit after the decimal is zero.

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Re: What is the reason why we do not count integers for sig figs?
Edward Tang 2E wrote:I think integer as a result of measurements are counted for sig figs, and the rules have been answered by previous students. Exact numbers derived from counting or integers that are defined numbers, however, aren't counted for sig fig because they do not affect the accuracy of calculation nor precision of expression. Say you counted 10 people in a room, you can express that with 10.0000 or 10.0000000000. Therefore technically there are an infinite number of sig figs in exact numbers so we just omit them entirely. However, if you measured the mass of an element to be 10 grams, you can't express that as 10.0 because the machine used is not calibrated to express the tenth; it would be inaccurate to assume that the digit after the decimal is zero.
Sorry, I'm a little confused on what you mean by not counting for sig fig. Like, do you mean when doing calculations?

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Re: What is the reason why we do not count integers for sig figs?
Yes, it depends on how precise your calculation is. For example, if your graduated cylinder measured to the hundredths place, you could measure exactly 100.00mL of water. But if the graduated cylinder only measured to the tenths place, you could measure exactly 100.0mL of water. Even if there is exactly 100.00mL in both, you can not be precisely sure.

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Re: What is the reason why we do not count integers for sig figs?
You only count zeroes when a decimal takes place (an exception if there there are zeroes without any number more than 0 before the decimal point for example 00.01. The two zero before the decimal are not counted towards sigfigs. However if it is 10.01, all numbers are counted towards sigfigs.) The main reason for this is because of the importance of precision and accuracy. Decimal places, even if it is at zero still has significant value when used to calculate.

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Re: What is the reason why we do not count integers for sig figs?
Jenny Chau 2L wrote:Edward Tang 2E wrote:I think integer as a result of measurements are counted for sig figs, and the rules have been answered by previous students. Exact numbers derived from counting or integers that are defined numbers, however, aren't counted for sig fig because they do not affect the accuracy of calculation nor precision of expression. Say you counted 10 people in a room, you can express that with 10.0000 or 10.0000000000. Therefore technically there are an infinite number of sig figs in exact numbers so we just omit them entirely. However, if you measured the mass of an element to be 10 grams, you can't express that as 10.0 because the machine used is not calibrated to express the tenth; it would be inaccurate to assume that the digit after the decimal is zero.
Sorry, I'm a little confused on what you mean by not counting for sig fig. Like, do you mean when doing calculations?
Yes. I believe say if part of your calculation includes converting 7.4 meters to centimeters by multiplying 7.4 by 100, the number 100 is omitted when determining how many sig figs the answer should have. So there should be two sig figs in your answer and not one, even though for multiplication your answer should have the same number of sig figs as one with the least sig figs.

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Re: What is the reason why we do not count integers for sig figs?
The scientific figures are created to help us simplify calculations. When to count the integers depend on the specific situations. Even though I don't fully understand your questions, I can still help you with something. For example, the number of sig figures for 300 is 1, the number of sig figures for 300.0 is 3, and the number of sig figues for 36 are two.
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